tim9000 said:
I've been trying to learn about cosmological expansion (some weeks ago), I think I understand as much as any lay-person could, regarding why everything is moving away from our galaxy. However I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing, but something that has tangible, observable properties. Such as in observing closer galaxies lens more distant galaxies, or that the Alcubierre drive is theoretically possible...or moreover that a 'big rip' could tear the electrons from atomic nuclei, if expansion accelerates.
So if the space part of spacetime itself is getting bigger, and for the aforementioned reasons space is presumably more than just a vacuum of quantum mechanical fluctuations (with various standard model fields in it). Then does humanity actually know what spacetime is, or is it still more or less a mystery?
Thank youP.S. I forgot, of course gravitational waves.
I would say that the fundamental observable phenomenon of space-time is the ability to measure distances, and time intervals. You can pretty much regard this as being done with rulers, and clocks. If you wax philosophical, you can probably agonize a lot over what a ruler and a clock really is. As far as science goes, we have an operational procedure based on the SI standard for measuring both.
I can dig up a quote for the "SI meter" and the "SI second" definition if one is needed, but it should be easy to find.
Space time is geometry, and we can regard geometry as the study of distances. Angles a a part of geometry, but if we have distances, we can compasses drawing circles, and we can imagine measuring distances along the arcs of these circles, and those define angles, so we can define angles in terms of distances. Thus we don't need to regard geometry as being about angles and distances, since we can define angles in terms of distance. We can regard geometry as being fundamentally about distances.
It's helpful to introduce the concept of coordinates to talk about geometry, though not strictly necessary. Since it's not strictly necessary, I will avoid it for now.
Space-time geometry takes a rather funny turn, in that there turns out not to be two separate sorts of distances (spatial distances and time distances, usually referred to as time intervals), but only one sort of "distance", an observer independent interval known at the Lorentz interval. The relationship between the Lorentz interval and the SI concepts of time interval and distance is one of the topics of special relativity, and the reason that we view space-time as a single unified entity rather than two separate concepts of space and time.
But you can compute the space-time interval knowing only how to measure distances and time intervals. So if you understand distances and time intervals, you have the tools needed to understand the Lorentz interval.
There are some tricky aspects about distance that I've glossed over, but the main point I'm trying to make is that you can regard space-time as being all about distances, and that we have operational procedures for measuring distance via instruments we call rulers and clocks.
